Mathematics
[ graduate program  courses  faculty ]
7018 Applied Physics and Mathematics
Building, Muir College
http://math.ucsd.edu
All courses, faculty listings, and curricular and degree requirements described herein are subject to change or deletion without notice. Updates may be found on the Academic Senate website: http://senate.ucsd.edu/catalogcopy/approvedupdates/.
The Undergraduate Program
The mathematics department offers a wide range of courses in pure and applied mathematics for its majors and for students in other disciplines. The department offers seven majors leading to the BS: mathematics, applied mathematics, mathematics—computer science, joint major in mathematics and economics, mathematics—scientific computation, mathematics—applied science and probability and statistics, and one leading to the BA: mathematics—secondary education. In addition, students can minor in mathematics or mathematics education. The department also has an Honors Program for exceptional students in any of the eight majors. See the sections on major programs and the other areas mentioned above as well as the course descriptions at the end of this section for more specific information about program requirements and the courses offered by the department. You may visit our website, http://math.ucsd.edu, for more information, including course web pages, career advising, and research interests of our faculty.
FirstYear Courses
Entering students must take the Mathematics Placement Exam (MPE) prior to orientation unless they have an appropriate score on an AP calculus exam, an appropriate score (600 for Math 10A; 650 for Math 20A) on the SAT II Math Level 2 exam, an appropriate score on the International Baccalaureate Higher Level Mathematics Exam, credit by means of a foreign exam (e.g. GCE), or transferable college credit in calculus. The purpose of the MPE is to recommend placement for entering students in Math 3C, 4C, 10A, or 20A. For more information about the MPE (test dates, test description, sample exams, online practice tests), see the Mathematics Testing and Placement website, http://mathtesting.ucsd.edu.
Prerequisites for Math 3C, 4C, 10ABC, 20ABCDEF, and 31AHBHCH are enforced through TritonLink. Students need to ensure that test scores and transferable college credit are submitted to the Registrar prior to enrollment through WebReg.
Math 3C is the department’s preparatory course for the Math 10 sequence, providing a review of algebraic skills, facility in graphing, and working with exponential and logarithmic functions.
Math 4C is the department’s preparatory course for the Math 20 sequence, providing a brief review of college algebra followed by an introduction to trigonometry and a more advanced treatment of graphing and functions.
Math 10ABC is one of three calculus sequences. The students in this sequence have completed a minimum of two years of high school mathematics. This sequence is intended for majors in liberal arts and the social and life sciences. It fulfills the mathematics requirements of Revelle College and the option of the generaleducation requirements of Muir College. Completion of two quarters fulfills the requirement of Marshall College and the option of Warren College and Eleanor Roosevelt College.
The second firstyear calculus sequence, Math 20ABC, is taken mainly by students who have completed four years of high school mathematics or have taken a college level precalculus course such as Math 4C. This sequence fulfills all college level requirements met by Math 10ABC and is required of many majors, including chemistry and biochemistry, bioengineering, cognitive science, economics, mathematics, molecular biology, psychology, MAE, CSE, ECE, and physics. Students with adequate backgrounds in mathematics are strongly encouraged to take Math 20 since it provides the foundation for Math 20DEF, which is required for some science and engineering majors.
Certain transfers between the Math 10 and Math 20 sequences are possible, but such transfers should be carefully discussed with an adviser. Able students who begin the Math 10 sequence and who wish to transfer to the Math 20 sequence, may follow one of three paths:
 Follow Math 10A with Math 20A, with two units of credit given for Math 20A. This option is not available if the student has credit for Math 10B or Math 10C.
 Follow Math 10B with Math 20B, receiving two units of credit for Math 20B.
 Follow Math 10C with Math 20B, receiving two units of credit for Math 20B and two units of credit for Math 20C.
Credit will not be given for courses taken simultaneously from the Math 10 and the Math 20 sequence.
The department also offers a threequarter Honors Calculus sequence in Multivariable and Vector Calculus and Linear Algebra. This sequence, Math 31AHBHCH, is designed for wellprepared students who have both a strong aptitude and a deep interest in mathematics and who wish to undertake a challenging series of courses. The sequence has a prerequisite of a score of 5 on the AP Calculus BC exam. These demanding, proofbased courses cover the material in Math 20F, 20C, and 20E respectively—and entering students with a 5 on the Calculus BC exam should consider starting in the Honors sequence if their major (or minor) program requires them to take, at least, Math 20ABC and 20F. Math majors who complete the entire threequarter honors sequence will have also satisfied the requirement of Math 109 for their major program. They would be able to replace Math 109 with any fourunit upperdivision mathematics elective course.
Major Programs
The department offers seven different majors leading to the BS: (1) mathematics, (2) applied mathematics, (3) mathematics—computer science, (4) joint major in mathematics and economics, (5) mathematics—scientific computation, (6) mathematicsapplied science, and (7) probability and statistics, and one leading to the BA: (1) mathematics—secondary education. The specific emphases and course requirements for these majors are described in the following sections. All majors must obtain a minimum 2.0 grade point average in the upperdivision courses used to satisfy the major requirements. Further, the student must receive a grade of C– or better in any course to be counted toward fulfillment of the major requirements. Any mathematics course numbered 100–194 may be used as an upperdivision elective. (Note: 195, 196, 197, 198, 199, and 199H cannot be used toward any mathematics major.) All courses used to fulfill the major must be taken for a letter grade. No more than three upperdivision courses taken externally from UC San Diego can be counted toward any major. Special exceptions may be considered via petition.
It is strongly recommended that all mathematics majors review their programs at least annually with a departmental adviser, and that they consult with the Advising Office in AP&M 6016 before making any changes to their programs. Current course offering information for the entire academic year is maintained on the department’s web page at http://www.math.ucsd.edu. Special announcements are also emailed to all majors.
Students who plan to go on to complete a PhD in mathematics should be advised that only the best and most motivated students are admitted. Many graduate schools expect that students will have completed a full sequence of abstract algebra (Math 100ABC) as well as a full sequence of analysis (Math 140ABC). The advanced Graduate Record Exam (GRE) often has questions that pertain to material covered in the last quarter of analysis or algebra. In addition, it is advisable that students consider Summer Research Experiences for Undergraduates. This is a program funded by the National Science Foundation to introduce students to math research while they are still undergraduates. In their senior year or earlier, students should consider taking some graduate courses so that they are exposed to material taught at a higher level. In their junior year, students should begin to think of obtaining letters of recommendation from professors who are familiar with their abilities.
Note: Math 20D, E, and F do not need to be taken in order. Math majors are strongly advised to take 20F as early as possible after successfully completing 20C.
Education Abroad
Students may be able to participate in the UC Education Abroad Program (EAP) and UC San Diego’s Opportunities Abroad Program (OAP) while still making progress toward the major. Students interested in this option should contact the Programs Abroad Office in the International Center and discuss their plans with the mathematics advising officer before going abroad.
The department must approve courses taken abroad. Information on EAP/OAP can be found in the “Education Abroad Program” section of the UC San Diego General Catalog and the website http://pao.ucsd.edu.
Major in Mathematics
The upperdivision curriculum provides programs for mathematics majors as well as courses for students who will use mathematics as a tool in the biological, physical and behavioral sciences, and the humanities.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students
completing Math 31CH may substitute a fourunit upperdivision mathematics
elective for Math 109.)
 One of the following sequences:
 Foundations of Real Analysis: Math 140AB
 Introduction to Analysis: Math 142AB and Math 120A (Math 140ABC recommended for graduate school)
 One of the following sequences:
 Abstract Algebra: Math 100AB
 Modern Applied Algebra: Math 103AB and Math 102 (Math 100ABC recommended for graduate school)
 Upperdivision electives to complete thirteen fourunit courses, chosen from any mathematics course numbered between 100 and 194 (including those taken from the requirements listed above)
As with all departmental requirements, more advanced courses on the same material may be substituted with written approval from the departmental adviser.
To be prepared for a strong major curriculum, students should complete the last three quarters of the 20 sequence and Math 109 before the end of their sophomore year. Either Math 140AB or 100AB should be taken during the junior year.
Major in Applied Mathematics
A major in applied mathematics is also offered. The program is intended for students planning to work on the interface between mathematics and other fields.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
 Programming (one of the following):
 CSE 8AALB (Intro to Computer Sci: Java)
 CSE 11 (Intro to Computer Sci: Java, Accelerated Pace)
 ECE 15 (Engineering Computation)
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Linear Algebra: Math 102 or Math 170A
 Analysis: Math 140AB or Math 142AB
 One of the following sequences:
 Math 180ABC, 181AB
 Math 180A, 181AB, and one from Math 181CE, 185
 Math 180ABC, 185
 Math 180A, 185, and any two from Math 170ABC, 175–179
 Math 183 and any three from Math 170ABC, 175–179
 One additional sequence which may be chosen from the list (#6) above or the following list: Math 110A120A130A, 110AB, 120AB, 152–184A, 154–184A, 155AB, 171AB, 193AB.
 Upperdivision electives to complete at least thirteen fourunit courses, chosen from any mathematics course numbered between 100 and 194 (including those taken from the requirements listed above) except
 Up to twelve units may be taken from outside the department in an approved applied mathematical area. A petition specifying the courses to be used must be approved by an applied mathematics adviser. No such units may also be used for a minor or program of concentration.
 MAE 107 and Econ 120ABC, cannot be counted toward the thirteen required courses.
To be prepared for a strong major curriculum, students should complete the last three quarters of the 20 sequence and Math 109 before the end of their sophomore year.
Major in Mathematics—Scientific Computation
This major is designed for students with a substantial interest in scientific computation. The program is a specialized applied mathematics program with a concentration in computer solutions of scientific problems.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
 Computer Programming: ECE 15and (CSE 8AALB or CSE 11)
 Basic Computation: Math 15A (or CSE 20) and Math 15B (or CSE 21) and CSE 12
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Linear Algebra: Math 102
 Probability and Statistics: Math 183 or 180A181A (Note: No credit for Math 183 if Math 180A or 181A taken prior or concurrently.)
 Analysis: Math 140AB or 142AB
 Numerical Analysis: Math 170ABC or Math 170AB, Math 175
 Optimization: Math 171AB
 Scientific Computing: Math 179

Additional elective upperdivision courses to total fifteen chosen from the following: Math 107AB, 110AB, 120AB, 130AB, 131, 152, 155AB, 170C, or 175.
At least fifteen upperdivision mathematics courses are required for the major, except  Up to three upperdivision courses may be taken outside the department in an approved scientific computation area in the sciences or engineering. A petition specifying the courses to be used must be approved by a mathematics—scientific computation adviser.
 MAE 107, Econ 120ABC, Math 195, 196, 197, 199, and 199H cannot be counted toward the thirteen fourunit upperdivision courses.
Major in Mathematics—Probability and Statistics
This major is designed for students with a substantial interest in probability theory and statistics. It is useful preparation for many fields of employment as well as graduate school.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
 Programming (one of the following):
 CSE 8AALB (Java)
 CSE 11 (Java: Accelerated Pace)
 ECE 15 (Engineering Computation)
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Linear Algebra: Math 102 or Math 170A
 Analysis/Advanced Calculus: Math 140AB or Math 142AB
 Numerical Methods: Math 174 or Math 170AB
 Probability: Math 180ABC
 Mathematical Statistics: Math 181AB
 One of the following: Math 181C, 181E, 193A, 193B, 194
 Computational Statistics: Math 185

Upperdivision electives to complete fifteen upperdivision courses from the following list: Math 100ABC, 103AB, 110AB, 120AB, 130A, 131, 140C, 152, 155AB, 170ABC, 171AB, 175, 176, 179, 181C, 181E, 184A, 187, 188, 193AB, 194
At least fifteen fourunit upperdivision mathematics courses are required, except  Two upperdivision electives may be outside the department in an approved applied mathematical area. A petition approved by a math adviser is required.
 MAE 107, Econ 120ABC, Math 195199 cannot be counted toward the upperdivision requirements.
To be prepared for a strong major curriculum, students should complete the last three quarters of the 20 sequence and Math 109 before the end of their sophomore year.
Major in Mathematics—Applied Science
This major is designed for students with a substantial interest in mathematics and its applications to a particular field such as physics, biology, chemistry, biochemistry, cognitive science, computer science, economics, management science, or engineering.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
 Programming (one of the following is required):
 CSE 8AALB (Intro to Computer Sci: Java)
 CSE 11 (Intro to Computer Sci: Java, Accelerated Pace)
 ECE 15 (Engineering Computation)
UpperDivision Mathematics Requirements
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Linear Algebra: Math 102 or Math 170A
 Analysis: Math 140AB or 142AB
 Any twoquarter, upperdivision math sequence
 Upperdivision electives to complete at least seven fourunit courses, chosen from any mathematics course numbered between 100 and 194 (including those taken from the requirements listed above)
UpperDivision Applied Science Requirements
 Seven upperdivision courses selected from one or two other departments (these cannot be from mathematics). At least three of these seven upperdivision courses must require calculus as a prerequisite.
Students must submit an individual plan for approval in advance by a mathematics department adviser, and all subsequent changes to the plan must be approved by a mathematics department adviser.
Major in Mathematics—Computer Science
Graduates of this program will be mathematically oriented computer scientists who have specialized in the mathematical aspects and foundations of computer science or in the computer applications of mathematics.
A mathematics—computer science major is not allowed to also minor in computer science in the Department of Computer Science and Engineering.
The detailed curriculum is given in the list below:
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
 CSE 8AALB Introduction to Computer Science: Java, or CSE 11 Introduction to Computer Science: Java (Accelerated)
 Basic Data Structures and ObjectOriented Design: CSE 12
 Computer Organization and Systems Programming: CSE 30 (Note: CSE 30 requires CSE 20 or Math 15A as a prerequisite.)
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Modern Applied Algebra: Math 103AB or Modern Algebra: Math 100AB
 Theory of Computability: Math 166 (or CSE 105)
 Intro to Probability: Math 180A or 183
 Combinatorics: Math 184A
 Computer Implementations of Data Structures: Math 176 (or CSE 100)
 Design and Analysis of Algorithms: Math 188 (or CSE 101)
 Eight units from Math 170ABC, 174, 175, 179 (Note duplication of credit between Math 174 and 170ABC)
 Eight units from Math 107AB, 152, 154, 155AB, 168AB, 187, CSE 120121, 130, 131AB, 140140L, 141141L, 167
 Eight additional units from any course in list #12 or #13 above or Math 102, 110AB, 111AB, 120AB, 130AB, 131, 140AB, 142AB, 150AB, 181ABC
Joint Major in Mathematics and Economics
Majors in mathematics and the natural sciences often feel the need for a more formal introduction to issues involving business applications of science and mathematics. Extending their studies into economics provides this application and can provide a bridge to successful careers or advanced study. Majors in economics generally recognize the importance of mathematics to their discipline. Undergraduate students who plan to pursue doctoral study in economics or business need the more advanced mathematics training prescribed in this major.
This major is considered to be excellent preparation for PhD study in economics and business administration, as well as for graduate studies for professional management degrees, including the MBA. The major provides a formal framework making it easier to combine study in the two fields.
Course requirements of the Joint Major in Mathematics and Economics consist principally of the required courses of the pure mathematics major and the economics/management science major.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDF
 Honors Calculus: Math 31AHBH, Math 20D
 Intro. to Economics: Econ 1 and 3
Upper Division
Fifteen upperdivision courses in mathematics and economics, with a minimum of seven courses in each department, chosen from the courses listed below (prerequisites are strictly enforced):
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 One of the following: Applied Linear Algebra: Math 102, Numerical Linear Algebra: Math 170A, Abstract Algebra: Math 100AB
 One of the following: Foundations of Real Analysis: Math 140A, Introduction to Analysis: Math 142A
 One of the following: Ordinary Differential Equations: Math 130A, Foundations of Real Analysis: Math 140B, Introduction to Analysis: Math 142B
 Microeconomics: Econ 100ABC
 Econometrics: Econ 120ABC or Math 180A and Econ 120BC or Math 180A, 181AB and Econ 120C
 One of the following:
 Macroeconomics: Econ 110AB
 Mathematical Programming: Numerical Optimization: Math 171AB
 Decisions Under Uncertainty: Econ 171
 Introduction to Operations Research: Econ 172AB, (Note: 172A is a prerequisite for 172BC.)
or two courses from the following:
Other courses which are strongly recommended are Math 130B, 131, 181B, 193AB and 194 and Econ 109, 113, 175, and 178.
Major in Mathematics—Secondary Education
This major offers excellent preparation for teaching mathematics in secondary schools. Students interested in earning a California teaching credential from UC San Diego should contact the Education Studies Program (EDS) for information regarding prerequisites and requirements. It is recommended you contact EDS as early as possible.
Required Courses
Lower Division
 One of the following sequences:
 Calculus: Math 20ABCDEF
 Honors Calculus: Math 31AHBHCH, Math 20D
Recommended:
 One of the following: Introduction to Computer Science: Java: CSE 8AALB, Engineering Computation: ECE 15
Upper Division
 Mathematical Reasoning: Math 109 (Note: Students completing Math 31CH may substitute a fourunit upperdivision mathematics elective for Math 109.)
 Number Theory: Math 104A
 History of Mathematics: Math 163
 Practicum in Learning: EDS 129ABC (can use EDS 136 and EDS 138 instead of EDS 129A)
 One of the following: Computer Algebra: Math 107A, Computer Graphics: Math 155A, Numerical Linear Algebra: Math 170A, Intro. to Cryptography: Math 187
 One of the following: Intro. to Probability: Math 180A, Statistical Methods: Math 183
 One of the following: Differential Geometry: Math 150A, Topics in Geometry: Math 151, Geometry for Secondary Teachers: Math 153, Intro. to Topology: Math 190
 One of the following: Abstract Algebra: Math 100A, Applied Linear Algebra: Math 102, Modern Applied Algebra: Math 103A
 One of the following: Foundations of Real Analysis: Math 140A, Introduction to Analysis: Math 142A

Upperdivision courses must total thirteen courses. Upperdivision
courses must include at least one twoquarter sequence from
the following list:
100AB; 103AB, 103A102; 104AB; 110AB; 110A120A; 110A130A; 110A131; 120AB; 140AB; 142AB; 150AB; 152184A; 154184A; 155AB; 160AB; 170AB; 170A175; 170A171A; 170A179; 171AB; 180AB; 180A181A; 193AB
Minor in Mathematics
The minor in mathematics consists of seven or more courses. At least four of these courses must be upperdivision courses taken from the UC San Diego Department of Mathematics. Acceptable lowerdivision courses are Math 20D, 20E (or 31CH), and 20F (or 31AH).
Math 195, 196, 197, 198, 199, and 199H are not acceptable courses for the mathematics minor. A grade of C– or better (or P if the Pass/Not Pass option is used) is required for all courses used to satisfy the requirements for a minor. There is no restriction on the number of classes taken with the P/NP option. Upperdivision courses cannot overlap between major and minor programs.
Minor in Mathematics Education
The mathematics education minor offered through the Education Studies program is intended for students interested in understanding how people learn mathematics, including: students considering K12 teaching as a career; students interested in teaching at the college level; and students who are interested in becoming better, more reflective learners. All majors are welcome, but the Calculus 10 or 20 sequence is a prerequisite for two of the upperdivision courses required for the minor. For more information contact Education Studies: http://physicalsciences.ucsd.edu/programs/calteach/matheducationminor.html.
Mathematics Honors Program
The Department of Mathematics offers an honors program for those students who have demonstrated excellence in the major. Successful completion of the honors program entitles the student to graduate with departmental honors (see Department Honors in the Academic Regulations section).
For Mathematics, Applied Mathematics, Mathematics—Scientific Computation, Mathematics—Applied Science, Mathematics—Secondary Education, Mathematics—Computer Science, and Probability and Statistics Majors
Requirements for admission to the program are
 Junior standing
 An overall GPA of 3.0 or higher
 A GPA in the major of 3.5 or higher
 Completion of Math 109 (Mathematical Reasoning) or Math 31CH (Honors Vector Calculus) and at least one of Math 100A, 103A, 140A, or 142A. (Completion of additional major courses is strongly recommended.)
Applications to the program should be made the spring quarter before the student is at senior standing.
Completion of the honors program requires the following:
 At least one quarter of the student colloquium, Math 196 (Note: Math 196 is only offered in the fall quarter.)
 The minimum 3.5 GPA in the major must be maintained
 An Honors Thesis. The research and writing of the thesis will be conducted over at least two quarters of the junior/senior years under the supervision of a faculty adviser. This research will be credited as eight to twelve units of Math 199H. The completed thesis must be approved by the department’s Honors Committee, and presented orally at the Undergraduate Research Conference or another appropriate occasion.
The department’s Honors Committee will determine the level of honors to be awarded, based on the student’s GPA in the major and the quality of the honors work. Applications for the mathematics department’s Honors Program can be obtained at the mathematics department Undergraduate Affairs Office (AP&M 7018) or the Mathematics Advising Office (AP&M 6016). Completed applications can be returned to the Mathematics Advising Office.
For Joint Mathematics and Economics Majors
To graduate with honors requires the following:
 At least one quarter of the Student Colloquium, Math 196 (Note: Math 196 is only offered in the fall quarter.)
 At least one Economics honors course: Econ 100AH, 100BH, 110AH, 110BH, 120AH, 120BH, 120CH. Note: Enrollment in these honors classes is by special permission; check with the undergraduate advisers in the Economics Student Services Office (SH 245).
 An Honors Thesis. The research and writing of the thesis will be conducted over two quarters of the senior year under the supervision of a faculty adviser. The completed thesis must be approved by the Joint Mathematics and Economics Honors Committee, which comprises the Mathematics Honors Committee and the Economics Honors Committee, and presented orally at the Undergraduate Research Conference or another appropriate occasion.
 If the student is a declared major in the mathematics department (MA33), this thesis will be credited as eight units of Math 199H. Enrollment in Math 199H is by special permission; check with the advisers in the mathematics department Undergraduate Affairs Office (AP&M 7018) or the Mathematics Advising Office (AP&M 6016).
 If the student is a declared major in the economics department (EN28), the student must enroll in Econ 191AB. Enrollment in Econ 191 is by special permission; check with the undergraduate advisers in the Economics Student Services Office (SH 245).
 A minimum GPA of 3.0 overall, 3.5 in the upperdivision courses required for the major and a 3.5 in the following four classes: Math 196, Economics Honors class and either Econ 191AB or two quarters of Math 199H.
The Joint Mathematics and Economics Honors Committee will determine the level of honors to be awarded, based on the student’s GPA in the major and the quality of the honors work.
Duplication of Credit
Information on duplication of credit (both full and partial) can be found in the course descriptions. It is the student’s responsibility to be aware of the credit restrictions listed.
Faculty Advisers
Advisers change yearly. Contact the undergraduate office at (858) 5343590 for current information.